Sufficient dimension reduction can aid the analysis of high-dimensional
microarray data by transforming the problems to low dimensional projections.
The curse of dimensionality is often alleviated, and the informative data
visualization may be enabled. In this talk, we start with an application of
a dimension reduction method, sliced inverse regression, to a microarray
survival data analysis. This exercise also introduces new challenges to
the methodology of sufficient dimension reduction, including the presence
of highly correlated predictors, the small-n-large-p problem, variable
selection in the framework of dimension reduction, and missing data in
predictors. We next continue the talk with a discussion of some recently
proposed dimension reduction methods to address the above challenges. Some
theoretical properties of the proposed methods will be explored, and the
analysis of the microarray data will underlie this line of methodology
development.